Domain.Math.Data.Relation

Type class

class Functor f => Relational f where

Minimal complete definition

leftHandSide, rightHandSide, flipSides, constructor

Methods

leftHandSide :: f a -> a

rightHandSide :: f a -> a

flipSides :: f a -> f a

constructor :: f a -> b -> b -> f b

isSymmetric :: f a -> Bool

Instances

Relational Inequality

Defined in Domain.Math.Data.Relation

Methods

leftHandSide :: Inequality a -> a

rightHandSide :: Inequality a -> a

flipSides :: Inequality a -> Inequality a

constructor :: Inequality a -> b -> b -> Inequality b

isSymmetric :: Inequality a -> Bool

Relational Equation

Defined in Domain.Math.Data.Relation

Methods

leftHandSide :: Equation a -> a

rightHandSide :: Equation a -> a

flipSides :: Equation a -> Equation a

constructor :: Equation a -> b -> b -> Equation b

isSymmetric :: Equation a -> Bool

Relational Relation

Defined in Domain.Math.Data.Relation

Methods

leftHandSide :: Relation a -> a

rightHandSide :: Relation a -> a

flipSides :: Relation a -> Relation a

constructor :: Relation a -> b -> b -> Relation b

isSymmetric :: Relation a -> Bool

Relation data type

data Relation a

Instances

Functor Relation

Defined in Domain.Math.Data.Relation

Methods

fmap :: (a -> b) -> Relation a -> Relation b

(<$) :: a -> Relation b -> Relation a

Foldable Relation

Defined in Domain.Math.Data.Relation

Methods

fold :: Monoid m => Relation m -> m

foldMap :: Monoid m => (a -> m) -> Relation a -> m

foldr :: (a -> b -> b) -> b -> Relation a -> b

foldr' :: (a -> b -> b) -> b -> Relation a -> b

foldl :: (b -> a -> b) -> b -> Relation a -> b

foldl' :: (b -> a -> b) -> b -> Relation a -> b

foldr1 :: (a -> a -> a) -> Relation a -> a

foldl1 :: (a -> a -> a) -> Relation a -> a

toList :: Relation a -> [a]

null :: Relation a -> Bool

length :: Relation a -> Int

elem :: Eq a => a -> Relation a -> Bool

maximum :: Ord a => Relation a -> a

minimum :: Ord a => Relation a -> a

sum :: Num a => Relation a -> a

product :: Num a => Relation a -> a

Traversable Relation

Defined in Domain.Math.Data.Relation

Methods

traverse :: Applicative f => (a -> f b) -> Relation a -> f (Relation b)

sequenceA :: Applicative f => Relation (f a) -> f (Relation a)

mapM :: Monad m => (a -> m b) -> Relation a -> m (Relation b)

sequence :: Monad m => Relation (m a) -> m (Relation a)

Relational Relation

Defined in Domain.Math.Data.Relation

Methods

leftHandSide :: Relation a -> a

rightHandSide :: Relation a -> a

flipSides :: Relation a -> Relation a

constructor :: Relation a -> b -> b -> Relation b

isSymmetric :: Relation a -> Bool

Eq a => Eq (Relation a)

Defined in Domain.Math.Data.Relation

Methods

(==) :: Relation a -> Relation a -> Bool

(/=) :: Relation a -> Relation a -> Bool

Ord a => Ord (Relation a)

Defined in Domain.Math.Data.Relation

Methods

compare :: Relation a -> Relation a -> Ordering

(<) :: Relation a -> Relation a -> Bool

(<=) :: Relation a -> Relation a -> Bool

(>) :: Relation a -> Relation a -> Bool

(>=) :: Relation a -> Relation a -> Bool

max :: Relation a -> Relation a -> Relation a

min :: Relation a -> Relation a -> Relation a

Show a => Show (Relation a)

Defined in Domain.Math.Data.Relation

Methods

showsPrec :: Int -> Relation a -> ShowS

show :: Relation a -> String

showList :: [Relation a] -> ShowS

Arbitrary a => Arbitrary (Relation a)

Defined in Domain.Math.Data.Relation

Methods

arbitrary :: Gen (Relation a)

shrink :: Relation a -> [Relation a]

CoArbitrary a => CoArbitrary (Relation a)

Defined in Domain.Math.Data.Relation

Methods

coarbitrary :: Relation a -> Gen b -> Gen b

IsTerm a => IsTerm (Relation a)

Defined in Domain.Math.Data.Relation

Methods

toTerm :: Relation a -> Term

toTermList :: [Relation a] -> Term

fromTerm :: MonadPlus m => Term -> m (Relation a)

fromTermList :: MonadPlus m => Term -> m [Relation a]

relationType :: Relation a -> RelationType

data RelationType

Constructors

EqualTo

NotEqualTo

LessThan

GreaterThan

LessThanOrEqualTo

GreaterThanOrEqualTo

Approximately

Instances

Enum RelationType

Defined in Domain.Math.Data.Relation

Methods

succ :: RelationType -> RelationType

pred :: RelationType -> RelationType

toEnum :: Int -> RelationType

fromEnum :: RelationType -> Int

enumFrom :: RelationType -> [RelationType]

enumFromThen :: RelationType -> RelationType -> [RelationType]

enumFromTo :: RelationType -> RelationType -> [RelationType]

enumFromThenTo :: RelationType -> RelationType -> RelationType -> [RelationType]

Eq RelationType

Defined in Domain.Math.Data.Relation

Methods

(==) :: RelationType -> RelationType -> Bool

(/=) :: RelationType -> RelationType -> Bool

Ord RelationType

Defined in Domain.Math.Data.Relation

Methods

compare :: RelationType -> RelationType -> Ordering

(<) :: RelationType -> RelationType -> Bool

(<=) :: RelationType -> RelationType -> Bool

(>) :: RelationType -> RelationType -> Bool

(>=) :: RelationType -> RelationType -> Bool

max :: RelationType -> RelationType -> RelationType

min :: RelationType -> RelationType -> RelationType

Show RelationType

Defined in Domain.Math.Data.Relation

Methods

showsPrec :: Int -> RelationType -> ShowS

show :: RelationType -> String

showList :: [RelationType] -> ShowS

Arbitrary RelationType

Defined in Domain.Math.Data.Relation

Methods

arbitrary :: Gen RelationType

shrink :: RelationType -> [RelationType]

CoArbitrary RelationType

Defined in Domain.Math.Data.Relation

Methods

coarbitrary :: RelationType -> Gen b -> Gen b

relationSymbols :: [(RelationType, (String, Symbol))]

notRelation :: Relation a -> Relation a

eval :: (Ord a, Num a) => RelationType -> a -> a -> Bool

Constructor functions

makeType :: RelationType -> a -> a -> Relation a

(.==.) :: a -> a -> Relation a infix 1

(./=.) :: a -> a -> Relation a infix 1

(.<.) :: a -> a -> Relation a infix 1

(.>.) :: a -> a -> Relation a infix 1

(.<=.) :: a -> a -> Relation a infix 1

(.>=.) :: a -> a -> Relation a infix 1

(.~=.) :: a -> a -> Relation a infix 1

Equation (or equality)

type Equations a = [Equation a]

data Equation a

Constructors

a :==: a infix 1

Instances

Functor Equation

Defined in Domain.Math.Data.Relation

Methods

fmap :: (a -> b) -> Equation a -> Equation b

(<$) :: a -> Equation b -> Equation a

Foldable Equation

Defined in Domain.Math.Data.Relation

Methods

fold :: Monoid m => Equation m -> m

foldMap :: Monoid m => (a -> m) -> Equation a -> m

foldr :: (a -> b -> b) -> b -> Equation a -> b

foldr' :: (a -> b -> b) -> b -> Equation a -> b

foldl :: (b -> a -> b) -> b -> Equation a -> b

foldl' :: (b -> a -> b) -> b -> Equation a -> b

foldr1 :: (a -> a -> a) -> Equation a -> a

foldl1 :: (a -> a -> a) -> Equation a -> a

toList :: Equation a -> [a]

null :: Equation a -> Bool

length :: Equation a -> Int

elem :: Eq a => a -> Equation a -> Bool

maximum :: Ord a => Equation a -> a

minimum :: Ord a => Equation a -> a

sum :: Num a => Equation a -> a

product :: Num a => Equation a -> a

Traversable Equation

Defined in Domain.Math.Data.Relation

Methods

traverse :: Applicative f => (a -> f b) -> Equation a -> f (Equation b)

sequenceA :: Applicative f => Equation (f a) -> f (Equation a)

mapM :: Monad m => (a -> m b) -> Equation a -> m (Equation b)

sequence :: Monad m => Equation (m a) -> m (Equation a)

Relational Equation

Defined in Domain.Math.Data.Relation

Methods

leftHandSide :: Equation a -> a

rightHandSide :: Equation a -> a

flipSides :: Equation a -> Equation a

constructor :: Equation a -> b -> b -> Equation b

isSymmetric :: Equation a -> Bool

Eq a => Eq (Equation a)

Defined in Domain.Math.Data.Relation

Methods

(==) :: Equation a -> Equation a -> Bool

(/=) :: Equation a -> Equation a -> Bool

Ord a => Ord (Equation a)

Defined in Domain.Math.Data.Relation

Methods

compare :: Equation a -> Equation a -> Ordering

(<) :: Equation a -> Equation a -> Bool

(<=) :: Equation a -> Equation a -> Bool

(>) :: Equation a -> Equation a -> Bool

(>=) :: Equation a -> Equation a -> Bool

max :: Equation a -> Equation a -> Equation a

min :: Equation a -> Equation a -> Equation a

Show a => Show (Equation a)

Defined in Domain.Math.Data.Relation

Methods

showsPrec :: Int -> Equation a -> ShowS

show :: Equation a -> String

showList :: [Equation a] -> ShowS

Arbitrary a => Arbitrary (Equation a)

Defined in Domain.Math.Data.Relation

Methods

arbitrary :: Gen (Equation a)

shrink :: Equation a -> [Equation a]

CoArbitrary a => CoArbitrary (Equation a)

Defined in Domain.Math.Data.Relation

Methods

coarbitrary :: Equation a -> Gen b -> Gen b

IsTerm a => IsTerm (Equation a)

Defined in Domain.Math.Data.Relation

Methods

toTerm :: Equation a -> Term

toTermList :: [Equation a] -> Term

fromTerm :: MonadPlus m => Term -> m (Equation a)

fromTermList :: MonadPlus m => Term -> m [Equation a]

equationView :: View (Relation a) (Equation a)

Inequality

data Inequality a

Constructors

a :<: a infix 1

a :>: a infix 1

a :<=: a infix 1

a :>=: a infix 1

Instances

Functor Inequality

Defined in Domain.Math.Data.Relation

Methods

fmap :: (a -> b) -> Inequality a -> Inequality b

(<$) :: a -> Inequality b -> Inequality a

Foldable Inequality

Defined in Domain.Math.Data.Relation

Methods

fold :: Monoid m => Inequality m -> m

foldMap :: Monoid m => (a -> m) -> Inequality a -> m

foldr :: (a -> b -> b) -> b -> Inequality a -> b

foldr' :: (a -> b -> b) -> b -> Inequality a -> b

foldl :: (b -> a -> b) -> b -> Inequality a -> b

foldl' :: (b -> a -> b) -> b -> Inequality a -> b

foldr1 :: (a -> a -> a) -> Inequality a -> a

foldl1 :: (a -> a -> a) -> Inequality a -> a

toList :: Inequality a -> [a]

null :: Inequality a -> Bool

length :: Inequality a -> Int

elem :: Eq a => a -> Inequality a -> Bool

maximum :: Ord a => Inequality a -> a

minimum :: Ord a => Inequality a -> a

sum :: Num a => Inequality a -> a

product :: Num a => Inequality a -> a

Traversable Inequality

Defined in Domain.Math.Data.Relation

Methods

traverse :: Applicative f => (a -> f b) -> Inequality a -> f (Inequality b)

sequenceA :: Applicative f => Inequality (f a) -> f (Inequality a)

mapM :: Monad m => (a -> m b) -> Inequality a -> m (Inequality b)

sequence :: Monad m => Inequality (m a) -> m (Inequality a)

Relational Inequality

Defined in Domain.Math.Data.Relation

Methods

leftHandSide :: Inequality a -> a

rightHandSide :: Inequality a -> a

flipSides :: Inequality a -> Inequality a

constructor :: Inequality a -> b -> b -> Inequality b

isSymmetric :: Inequality a -> Bool

Show a => Show (Inequality a)

Defined in Domain.Math.Data.Relation

Methods

showsPrec :: Int -> Inequality a -> ShowS

show :: Inequality a -> String

showList :: [Inequality a] -> ShowS

Arbitrary a => Arbitrary (Inequality a)

Defined in Domain.Math.Data.Relation

Methods

arbitrary :: Gen (Inequality a)

shrink :: Inequality a -> [Inequality a]

CoArbitrary a => CoArbitrary (Inequality a)

Defined in Domain.Math.Data.Relation

Methods

coarbitrary :: Inequality a -> Gen b -> Gen b

IsTerm a => IsTerm (Inequality a)

Defined in Domain.Math.Data.Relation

Methods

toTerm :: Inequality a -> Term

toTermList :: [Inequality a] -> Term

fromTerm :: MonadPlus m => Term -> m (Inequality a)

fromTermList :: MonadPlus m => Term -> m [Inequality a]

inequalityView :: View (Relation a) (Inequality a)